Scanning Tunneling Microscopy how does STM work? the quantum mechanical picture example of images how can we understand what we see?
Observation of adatom diffusion with a field ion microscope
Scanning Tunneling Microscope
wavefunction of electron in metal wavefunction of electron in metal 1 metal-insu.-metal wavefunction after tunneling through barrier tunneling through a rectangular barrier the work function forms the barrier between a surface and vacuum wavefunction decay at surface (single, infinitely wide barrier) overlap of electron wavefunctions from both sides of the barrier wavefunction of electron in metal 2 contact formation - tunneling probability large enough for current to be measured
Scanning Tunneling Microscopy applied bias voltage: E F2 -E F1
DENSITY OF STATES g(e) g(e) Number of states / unit energy interval / unit vol. g(e) de Number of states in range E to E+dE per unit vol. FERMI ENERGY E F Proper definition: The energy at which the probability of an electron occupying a given state is ½; f(e F ) = 1/2 Loose definition The highest occupied energy state at 0 K (okay for metals, not semiconductors, where E F is in forbidden zone - bandgap )
The quantum mechanical description of STM ε = states which contribute to tunneling Fermi function tunneling from filled states states to tunnel into overlap of wavefunctions only integration from 0 to ev an excerpt from: Tersoff et al, Phys. Rev. Lett. 50,1998, Phys. Rev. B 31, 805 discussed in: Lab on a tip by Meyer
we usually assume: the tip has a spherical shape and charge distribution and does not change during a measurement. Its contribution to the tunneling process is therefore constant and change in the current can solely attributed to the sample. Tungsten tips have in reality occuppied d-states which are not spherical (check out the shape of d-orbitals in your chemistry book), and in some instances with very high resolution and low temperatures the tip can actually be imaged.
The Tersoff-Hamann model to describe tip-sample interaction three dimensional geometry tip wave function decribed by s-wave (spherical) the LDOS of the sample at the center of the tip (s+r) is used for the tunneling current the local density of states at the Fermi level is decisive
Demonstration of Vacuum Tunneling measurement of current as a function of distance between sample and tip logarithmic dependence of current on distance illustrates that tunneling process determines the current the slope is related to the barrier height (and thus the work function ) change in barrier height throughout experiment due to change in cleanliness of sample surface (or tip) G. Binnig, H. Rohrer, Helv. Phys. Acta 55, 726
Modes of Operation STM scanning tunneling microscopy constant voltage applied to tip, topography images STS - scanning tunneling spectroscopy voltage between tip and sample is changed during measurement this is like a current-voltage characteristics. The derivative of this I- V curve is then proportional to the DENSITY OF STATES and the related to the ELECTRONIC STRUCTURES
Switching VO 2 : the view from the surface Abrupt structural phase transition from monoclinic (insulator) to tetragonal (metal) phase at 341 K tetragonal/metal 39.80 2! 39.75 39.70 T 39.65 T 39.60 300 350 400 450 temperature (K) monoclinic insulator
296K, 0.2V 325K, 0.2V 360K, 0.2V (a) (b) (c)
Graphite Surface distance between light points 0.246 nm C-C bond length in graphite: 0.146 nm from: Zangwil, Surface Science
Graphite Surface distance between light points 0.246 nm C-C bond length in graphite: 0.146 nm from: Zangwil, Surface Science
Graphite Surface α (white) above next layer atom β - (red) above hollow site http://www.physik.uni-regensburg.de/forschung/giessibl/fjg/ imagegallery/afmimages/afmimages_d.shtml AFM image shows the hidden carbon atom! PNAS_100_12539 calculated STM image
Detour: Surface Reconstruction
Surfaces of Elemental Semiconductors - Si-Ge-GaAs silicon and germanium: coordination 4 face centered cubic lattice basis with two atoms per unit cell lattice constant: 5.43 Å for Si 5.65 Å for Ge GaAs zinc blende lattice basis with two atoms per unit cell As Ga ZnS lattice often found for III-V semiconductors
Silicon (100) minimizing the number of dangling bonds: dimer formation between adjacent Si atoms
Buckled Dimers and Flip-Flop Motion filled state STM image at 63 K buckling of dimers (not horizontal but tilted by 18 ) disorder-order tranistion at 200 K (correlated buckling in diagramm) c(2x1) transformed to c(4x2) and amtiphase ordering of buckled dimers but symmetric appearance of dimers at 5 K (apparent disappearance of dimers): attributed to thermal stress induced flip-flop motion of dimers
Silicon (111) Si (111) cleavage plane 2x1 metastable 400 7x7 DAS structure 850 order-disorder transition 1x1
End Detour: Surface Reconstruction
bulk like termination: 49 dangling bonds in 7x7 mesh; (7x7) DAS reconstruction: 12 adatoms + 6 restatoms + corner holes per unit cell = 19 dangling bonds.
Scanning Tunneling Spectroscopy (variation of applied voltage) experimental conditions: (1) repeated measurement of complete area with constant current and different V (2) complete I-V curve for each pixel of scan 1.6 V tunneling into empty states -1.6 V tunneling from filled states 20x20 nm constant current (pg. 185)
Imaging different atoms on the Si(111)7x7 surface constant current image topography (2V) constant height image I-V curve for every raster point in const. current image -0.35 V adatom state (surface state) -0.8 V dangling bond -1.7 V backbond state PRL-56-1972
Surface States on the Si(111) 7x7 surface - surface bands and reconstruckon shows integrakon over area of sample locally resolved surface states - assignment to different bonding sites possible
... back to VO 2... BG >= 0.4 ev Metallic 293 K! IMT at 337 K! 349 K!
sample: Pt 25 Ni 75 (111) single crystal surface measurement in constant current mode with positive tip bias observed corrugation larger than differences in atoms radius (only for not extremely clean surface!) both metals similar DOS at Fermi energy Chemical sensitivity on an alloy surface interpretation: adsorbate at tip interacts stronger with one element and thus yields a larger corrugation in constant current image observation: surface shows short range ordering large corrugation of surface observed under these conditions (not very clean surface) PRL_70_1441
Nature_403_512_quantum mirage RevModPhys.75.933 review on quantum corrals
The STM as a tool: manipulation of adatoms Pb, CO and Cu positioned on a Cu (211)surface a side view of the adatoms note the different adsorption sites... and an ideal, atomically sharp tip PRL_79_697
fcc site The STM as a tool: manipulation of adatoms PULLING Sliding - dotted line is fcc site next to step edge - arrow in STM image of adsorbate indicate tip direction - note: the measurements are done at 30K - procedure: moving tip to initial point, setpoint current is increased leading to much smaller distance between tip and surface, tip then moved at constant current while recording the distance variation (trace in graph) - attractive forces between tip and adatom are used to advance adatom (pulling) - local probe for energy landscape on surface
Detour: Surface States
Bulk and Surface Band Structure solving the Schrödinger equakon in three dimensions yields the bulk band structure if a surface is introduced the boundary condikons change and the 2D solukons are obtained shaded area: bulk band structure projected onto the surface broken lines: surface band structure
The Surface Electron Band Structure Shockley State: located in band gap of bulk band structure solukon of Schrödinger equakon in nearly- free electron model (good for metals) Cu(111) band structure Brillouin zone center s- p band Tamm State: obtained from solukon of Kght- binding model (o_en used for semiconductors, insulators, uses model similar to atomic orbital descripkon) the two types of surface states are not physically dis4nct, but arise from a different descripkon of the surface band structure Brillouin zone boundary d band
End Detour: Surface States
The smallest nanostructures - a quantum corral Fe atoms arranged on a Cu(111) surface positioned and measured with a scanning tunneling microscope The quantum corral is an excellent example for atomic scale assembly, and probing of nanoscale structures. At the same time it allowed for the first time to visualize an electron wave which is confined by the quantum corral Crommie, Lutz & Eigler hcp://www.almaden.ibm.com/vis/stm/corral.html 37
Directional Control in Thermally Driven Single-Molecule Nanocars Nanoletters, 5 2330 (2005) goal: rolling motion of molecule with fullerene molecules as wheels molecule was designed with this goal in mind molecules are adsorbed on a Au-surface
observing the molecule motion with an STM series of Kme- lapse images taken at 200ºC one minute time lapse images molecules become mobile at T>170ºC thermally induced motion is osberved here combination of pivot and translational motion L1_1D_Science_266_1979_nanosled_AFM
pushing the nanocar with the STM tip pushing leads for other organic molecules to a displacement along the direction of the push for the nanocar the direction of the move is determined by the stiffness of the axle and leads to an arc-like motion [very similar to the action of a cart when pushed] conclusions: the nanocar movement is very similar to that of a macroscopic cart with a similar axle arrangement and rolling wheels